Sentence examples for be proved that if from inspiring English sources

If ZF′ denotes the theory obtained from ZF by deleting AR and either retaining or deleting the axiom of choice (AC), then it can be proved that, if ZF′ is consistent, AR is independent of ZF′.

It can be proved that, if these sums and products are properly specified, the fundamental laws of arithmetic hold for these pairs and that the pairs of the type (a, 1) are abstractly identical with the positive integers a.

Finally it will be proved that if T belongs to the k-quasi-∗-class and is a contraction, then T has a Wold-type decomposition and T has the PF property.

end{aligned}Also for the s-perimeter balls are the isoperimetric sets, since it can be proved that if (Esubset mathbb {R}^n) is a measurable set with (|E|=|B_r|) for some (r>0), then begin{aligned} P_s(B_r)le P_s(E) end{aligned} (5.42 with equality holding if and only if E is a ball.

Indeed, it can be proved that if D E) is smaller than some positive (delta ) depending only on n one may remove from E a small critical set, whose measure is controlled by D E), such that outside this critical set a Poincaré inequality holds true with a constant depending only on n.

It can be proved that if each Q s, a) value can be updated through an infinite number of iterations, and in this process in some appropriate way α gradually reduced to 0, Q s, a) will converge to the optimal value of the probability of a Q* s, a).

It can be proved that is a solution of (2.11) if and only if satisfies the operator equation.

By using the method in [10] mutatis mutandis, it can easily be proven that, if (fin C [0,1]times[0,+infty ),[0,+infty))), then the boundary value problem given by Eqs.

The trick is maintaining the quality, and 2tor may be proving that if startups aren't willing to take the long-view, and get the necessary capital backing, it'll be an uphill climb.

It is proved that if an invertible operator belongs to D (scAδ), then its inverse also belongs to D (scAδ).

It is proved that if the system is observable, such a reconstruction is always possible if the eigenvalues of the system are all real valued.